Updated determination of $D^0–{\overline{D}}^0$ mixing and $CP$ violation parameters with $D^0\to K^{+}{\pi }^{-}$ decays

We report measurements of charm-mixing parameters based on the decay-time-dependent ratio of $D^0\to K^{+}{\pi }^{-}$ to $D^0\to K^{-}{\pi }^{+}$ rates. The analysis uses a data sample of proton-proton collisions corresponding to an integrated luminosity of $5.0{\mathrm{fb}}^{-1}$ recorded by the LHCb experiment from 2011 through 2016. Assuming charge-parity ($CP$) symmetry, the mixing parameters are determined to be $x^{\prime 2}=(3.9\pm 2.7)\times {10}^{-5}$, $y^{\prime }=(5.28\pm 0.52)\times {10}^{-3}$, and $R_D=(3.454\pm 0.031)\times {10}^{-3}$. Without this assumption, the measurement is performed separately for $D^0$ and ${\overline{D}}^0$ mesons, yielding a direct $CP$-violating asymmetry $A_D=(-0.1\pm 9.1)\times {10}^{-3}$, and magnitude of the ratio of mixing parameters $1.00<|q/p|<1.35$ at the 68.3% confidence level. All results include statistical and systematic uncertainties and improve significantly upon previous single-measurement determinations. No evidence for $CP$ violation in charm mixing is observed.

Figure 1

Distribution of $M(D^0{\pi }_{\mathrm{s}}^{+})$ for selected (a) right-sign $D^0\to K^{-}{\pi }^{+}$ and (b) wrong-sign $D^0\to K^{+}{\pi }^{-}$ candidates.

Figure 2

Efficiency-corrected ratios of WS-to-RS yields for (a) $D^{*+}$ decays, (b) $D^{*-}$ decays, and (c) their differences as functions of decay time in units of $D^0$ lifetime. Projections of fits allowing for (dashed line) no $CP$ violation, (dotted line) no direct $CP$ violation, and (solid line) direct and indirect $CP$ violation are overlaid. The last two curves overlap. The abscissa of each data point corresponds to the average decay time over the bin. The error bars indicate the statistical uncertainties.

Figure 3

Two-dimensional confidence regions in the $(x^{\prime 2},y^{\prime })$ plane obtained (a) without any restriction on $CP$ violation, (b) assuming no direct $CP$ violation, and (c) assuming $CP$ conservation. The dashed (solid) curves in (a) and (b) indicate the contours of the mixing parameters associated with ${\overline{D}}^0$ ($D^0$) decays. The best-fit value for ${\overline{D}}^0$ ($D^0$) decays is shown with an open (filled) point. The solid, dashed, and dotted curves in (c) indicate the contours of $CP$-averaged mixing parameters at 68.3%, 95.5%, and 99.7% confidence levels (C.L.), respectively, and the point indicates the best-fit value.